Re: [math-fun] Another(?) stick length illusion
Huh? At least to the nearest pixel, both lines are the same length. They are corresponding diagonals of congruent regular pentagons. I find this to be an impressive illusion. --Dan << << To me the stick that is in fact longer looks like it is in fact longer. If they're supposed to be the same length I think your image needs a bit of editing.
On Thu, Aug 19, 2010 at 4:31 PM, Bill Gosper <billgosper@gmail.com> wrote:
While hacking the pentagon fill, tutor Julian found www.tweedledum.com/rwg/6pents.png, which seems to work backwards: The stick larger than its context appears smaller than the stick smaller than its context.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
What is your experimental method, guys? I copied the image into Adobe Illustrator and used the measuring tool to check. The leftward segment measured 4.05", and the rightward segment measured 4.17". A 3% difference. Theoretical equality != actual equality. I suspect this has to do with how pentagons were rendered. Are they areas with edges set to be the same color as the interior? If so, the added edge-thickness adds more where there's a shallow angle than where there's a wide angle. If I'm not mistaken, this would be (Sin[4 pi/10)-Sin(pi/10)) * 2 (width of line that overshoots past pentagon) ~ 1.3 x (thickness of overshoot). If blending-in borders are either a bit more than twice as thick as the .04" wide black line segments, or about the same thickness and drawn completely outside (rather than centered), that would approximately account for the difference. It's primarily a mathematical illusion, not a visual illusion. Bill T On Aug 19, 2010, at 11:17 PM, Dan Asimov wrote:
Huh? At least to the nearest pixel, both lines are the same length. They are corresponding diagonals of congruent regular pentagons.
I find this to be an impressive illusion.
--Dan
<< << To me the stick that is in fact longer looks like it is in fact longer. If they're supposed to be the same length I think your image needs a bit of editing.
On Thu, Aug 19, 2010 at 4:31 PM, Bill Gosper <billgosper@gmail.com> wrote:
While hacking the pentagon fill, tutor Julian found www.tweedledum.com/rwg/6pents.png, which seems to work backwards: The stick larger than its context appears smaller than the stick smaller than its context.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
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On Thu, Aug 19, 2010 at 8:44 PM, Bill Thurston <wpt4@cornell.edu> wrote:
What is your experimental method, guys? I copied the image into Adobe Illustrator and used the measuring tool to check. The leftward segment measured 4.05", and the rightward segment measured 4.17". A 3% difference. Theoretical equality != actual equality.
My experimental method was somewhat cruder: I held up a piece of paper next to one line on my screen, made two marks, then slid the paper over. Going back and forth a few times convinced me that it wasn't just pencil mark error. --Joshua
gosper.org/Muller-Liar.gif [2] (Subj. was: (_|_) and 6pents) On 2010-08-19 20:17, Dan Asimov wrote:
Huh? At least to the nearest pixel, both lines are the same length. They are corresponding diagonals of congruent regular pentagons.
I find this to be an impressive illusion.
--Dan
<< << To me the stick that is in fact longer looks like it is in fact longer. If they're supposed to be the same length I think your image needs a bit of editing.
On Thu, Aug 19, 2010 at 4:31 PM, Bill Gosper <billgosper@gmail.com> wrote:
While hacking the pentagon fill, tutor Julian found www.tweedledum.com/rwg/6pents.png [1], which seems to work backwards: The stick larger than its context appears smaller than the stick smaller than its context.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
Links: ------ [1] http://www.tweedledum.com/rwg/6pents.png [2] http://ma.sdf.org/gosper.org/Muller-Liar.gif
This now strikes me as a MUCH MORE impressive illusion than at first!!! Because whenever I stare at one line, then switch to the other, the second one always seems longer! Regardless of which one was first! —Dan
On Aug 25, 2015, at 1:19 AM, rwg <rwg@sdf.org> wrote:
gosper.org/Muller-Liar.gif [2] (Subj. was: (_|_) and 6pents)
On 2010-08-19 20:17, Dan Asimov wrote:
Huh? At least to the nearest pixel, both lines are the same length. They are corresponding diagonals of congruent regular pentagons.
I find this to be an impressive illusion.
--Dan
<< << To me the stick that is in fact longer looks like it is in fact longer. If they're supposed to be the same length I think your image needs a bit of editing.
On Thu, Aug 19, 2010 at 4:31 PM, Bill Gosper <billgosper@gmail.com> wrote:
While hacking the pentagon fill, tutor Julian found www.tweedledum.com/rwg/6pents.png [1], which seems to work backwards: The stick larger than its context appears smaller than the stick smaller than its context.
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
Links: ------ [1] http://www.tweedledum.com/rwg/6pents.png [2] http://ma.sdf.org/gosper.org/Muller-Liar.gif _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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